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Magnetic Resonance Imaging (MRI) is a powerful imaging technique widely used for visualizing structures within the human body and in other fields such as plant sciences. However, there is a demand to develop fast 3D-MRI reconstruction…

Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based…

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…

Despite the remarkable progress in generative modelling, current diffusion models lack a quantitative approach to assess image quality. To address this limitation, we propose to estimate the pixel-wise aleatoric uncertainty during the…

Magnetic resonance imaging (MRI) is a widely used non-invasive imaging modality. However, a persistent challenge lies in balancing image quality with imaging speed. This trade-off is primarily constrained by k-space measurements, which…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

Magnetic Resonance Imaging (MRI) is an essential diagnostic tool in clinical settings but its utility is often hindered by noise artifacts introduced during the imaging process. Effective denoising is critical for enhancing image quality…

Diffusion MRI (dMRI) is essential for studying brain microstructure, but high-resolution imaging remains challenging due to the inherent trade-offs between acquisition time and signal-to-noise ratio (SNR). Conventional methods often…

A near-optimal reconstruction of the radiance of a High Dynamic Range scene from an exposure stack can be obtained by modeling the camera noise distribution. The latent radiance is then estimated using Maximum Likelihood Estimation. But…

We propose a regression model for non-central $\chi$ (NC-$\chi$) distributed functional magnetic resonance imaging (fMRI) and diffusion weighted imaging (DWI) data, with the heteroscedastic Rician regression model as a prominent special…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…

This paper presents a fast computational method, the Expectation Maximization algorithm, for Maximum Likelihood (ML) estimation in diffusion tensor imaging under the Rice noise model. We further extend the ML framework to the maximum a…

Accelerated MRI reconstruction involves solving an ill-posed inverse problem where noise in acquired data propagates to the reconstructed images. Noise analyses are central to MRI reconstruction for providing an explicit measure of solution…

Magnetic resonance (MR) images from multiple sources often show differences in image contrast related to acquisition settings or the used scanner type. For long-term studies, longitudinal comparability is essential but can be impaired by…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…

We make use of recent results from random matrix theory to identify a derived threshold, for isolating noise from image features. The procedure assumes the existence of a set of noisy images, where denoising can be carried out on individual…

Over recent years, deep learning based image registration has achieved impressive accuracy in many domains, including medical imaging and, specifically, human neuroimaging with magnetic resonance imaging (MRI). However, the uncertainty…